A functorial approach to n -abelian categories
Year: 2025
Type: article
Abstract: We develop a functorial approach to the study of n -abelian categories by reformulating their axioms in terms of their categories of finitely presented functors. Such an approach allows the use of classical homological algebra and representation theory techniques to understand higher homological algebra. As an application, we present two possible generalizations of the axioms “every monomorphism is a kernel” and “every epimorphism is a cokernel” of an abelian category to n -abelian categories. We also specialize our results to modules over rings, thereby describing when the category of finitely generated projective modules over a ring is n -abelian. Moreover, we establish a correspondence for n -abelian categories with additive generators, which extends the higher Auslander correspondence.
Source: Comptes Rendus Mathématique
DOI: 10.5802/crmath.790
Author: Vitor Gulisz
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4415104285